Figure: Most studies of cortical network dynamics are either based on purely random wiring or neighborhood couplings, e.g., [Kumar, Schrader, Aer tsen, Rotter, 2008, Neural Computation 20, 1--43]. Neuronal connections in the cortex, however, show a complex spatial pattern composed of local and long-range connections, the latter featuring a so-called patchy projection pattern, i.e., spatially clustered synapses [Binzegger, Douglas, Martin, 2007, J. Neurosci. 27(45), 12242--12254]. The idea of our project is to provide and to analyze probabilistic network models that more adequately represent horizontal connectivity in the cortex. In particular, we investigate the effect of specific projection patterns on the dynamical state space of cortical networks. Assuming an enlarged spatial scale we employ a distance dependent connectivity that reflects the geometr y of dendrites and axons. We simulate the network dynamics using a neuronal network simulator NEST/PyNN. Our models are composed of conductance based integrate-and-fire neurons, representing fast spiking inhibitor y and regular spiking excitator y cells. In order to compare the dynamical state spaces of previous studies with our network models we consider the following connectivity assumptions: purely random or purely local couplings, a combination of local and distant synapses, and connectivity structures with patchy projections. Similar to previous studies, we also find different dynamical states depending on the input parameters: the external input rate and the numerical relation between excitatory and inhibitory synaptic weights. These states, e.g., synchronous regular (SR) or asynchronous irregular (AI) firing, are characterized by measures like the mean firing rate, the correlation coefficient, the coefficient of variation and so forth. On top of identified biologically realistic background states (AI), stimuli are applied in order to analyze their stability. Comparing the results of our different network models we find that the parameter space necessary to describe all possible dynamical states of a network is much more concentrated if local couplings are involved. The transition between different states is shifted (with respect to both input parameters) and sharpened in dependence of the relative amount of local couplings. Local couplings strongly enhance the mean firing rate, and lead to smaller values of the correlation coefficient. In terms of emergence of synchronous states, however, networks with local versus non-local or patchy versus random remote connections exhibit a higher probability of synchronized spiking. Concerning stability, preliminary results indicate that again networks with local or patchy connections show a higher probability of changing from the AI to the SR state. We conclude that the combination of local and remote projections bears important consequences on the activity of network: The apparent differences we found for distinct connectivity assumptions in the dynamical state spaces suggest that network dynamics strongly depend on the connectivity structure. This effect might be even stronger with respect to the spatio-temporal spread of signal propagation.

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